Simple Harmonic Motion: Determine Velocity at t=0.250s

In summary, the conversation discusses determining the velocity of a 39.8 g oscillating mass at t=0.250s using the equation x(t)= (2.00cm)cos(5t- 4.00\pi). The attempt at a solution involves substituting the given values into the formula V_{x}= -\omegaAsin(\omegat + \phi), but there was some confusion with units. The basic relation connecting velocity and position is also mentioned.
  • #1
Moe*
10
0
_{}b]1. Homework Statement [/b)

The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00[tex]\pi[/tex]) where t is in seconds. Determine Velocity at t= 0.250s

M= 39.8 g
T= 1.2575 rad/s
K= 9.95e-1 N/m
initial postion= 2 cm

Homework Equations



V[tex]_{x}[/tex]= -[tex]\omega[/tex]Asin([tex]\omega[/tex]t + [tex]\phi[/tex])

The Attempt at a Solution



the attempt i just substitued
V[tex]_{x}[/tex]= -5 rad/s*2sin( 5.00(0.250)-4[tex]\pi[/tex])... but this didn't work and i don't understand why?
 
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  • #2
for the the equations posted its supposed to be V subscript x= wAsin(wt + phi) and x(t) = (2.00cm)cos(5t - 4pi)
 
  • #3
Moe* said:
The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00[tex]\pi[/tex]) where t is in seconds. Determine Velocity at t= 0.250s

What is the basic relation connecting velocity and position of any particle? Use that.
 
  • #4
Moe* said:
_{}b]1. Homework Statement [/b)

The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00[tex]\pi[/tex]) where t is in seconds. Determine Velocity at t= 0.250s

M= 39.8 g
T= 1.2575 rad/s
K= 9.95e-1 N/m
initial postion= 2 cm

Homework Equations



V[tex]_{x}[/tex]= -[tex]\omega[/tex]Asin([tex]\omega[/tex]t + [tex]\phi[/tex])

The Attempt at a Solution



the attempt i just substitued
V[tex]_{x}[/tex]= -5 rad/s*2sin( 5.00(0.250)-4[tex]\pi[/tex])... but this didn't work and i don't understand why?
it seems work to me...
 
  • #5
Your right it does work, i guess I entered in the wrong units when i answered the question( m/s instead of cm/s).
 

Related to Simple Harmonic Motion: Determine Velocity at t=0.250s

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion in which an object moves back and forth in a straight line, with a restoring force proportional to the displacement from its equilibrium position.

2. What causes Simple Harmonic Motion?

SHM is caused by a restoring force, typically provided by a spring or elastic material, that acts in the opposite direction of the displacement of the object from its equilibrium position.

3. What are the key characteristics of Simple Harmonic Motion?

The key characteristics of SHM include a constant period (time for one complete oscillation), a sinusoidal displacement graph, and a maximum velocity at the equilibrium position.

4. How is Simple Harmonic Motion related to Hooke's Law?

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the object from its equilibrium position. This is the restoring force that enables SHM.

5. What are some real-life examples of Simple Harmonic Motion?

Some examples of SHM include the motion of a pendulum, the vibrations of a guitar string, and the back-and-forth motion of a mass on a spring. SHM can also be observed in the motion of a car's suspension system or the swinging of a playground swing.

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